**5.N Understand and use numeration**

**5.N-1 reading, writing, ordering, or counting****5.N-2 identifying place value positions from tenths to millions****5.N-3 converting between whole numbers written in expanded notation and standard form****5.N-4 modeling, identifying, describing with explanations, or illustrating equal parts of a whole, a region, or a set****5.N-5 modeling, identifying, describing with explanations, or illustrating equivalent fractions or mixed numbers**- Decimals: Convert fractions to decimals (Fifth grade - C.9)
- Decimals: Convert decimals to fractions (Fifth grade - C.10)
- Fractions and mixed numbers: Equivalent fractions (Fifth grade - L.2)
- Fractions and mixed numbers: Reduce fractions to simplest form (Fifth grade - L.3)
- Fractions and mixed numbers: Convert between improper fractions and mixed numbers (Fifth grade - L.4)
- Ratios, proportions, and percents: Convert between percents, fractions, and decimals (Fifth grade - V.9)

**5.N-7 using models, explanations, number lines, or real-life situations describing or illustrating the process of adding and subtracting proper fractions or mixed numbers (like denominators)****5.N-8 using models, explanations, number lines, or real-life situations describing or illustrating the process of adding or subtracting decimals that represent money****5.N-9 describing or illustrating commutative or identity properties of addition or multiplication using models or explanations****5.N-10 identifying or listing factors and multiples common to a pair or set of numbers****5.MEA-1 estimating length to the nearest one-fourth inch or centimeter****5.MEA-2 estimating temperature (degree Celsius or Fahrenheit, plus or minus 5 degrees) or weight (half-pounds or kilograms) to the nearest unit****5.MEA-3 identifying or using equivalent measures for weight/mass (16 oz. = 1 pound or 1000 grams = 1 kilogram) and length (1000 millimeters = 1 meter) or time****5.MEA-5 telling time using analog clocks to the nearest minute and using A.M. or P.M.****5.MEA-6 determining possible combinations of coins and bills to given amounts****5.MEA-7 simulating multiple purchases and calculating the amount of change from given bills up to $100.00****5.E&C-1 identifying or using a variety of strategies (e.g., rounding to appropriate place value, multiplying by powers of ten, using front-end estimation to estimate the results of addition or subtraction computations from tenths to 100,000, including money, or simple multiplication or division**- Decimals: Round decimals (Fifth grade - C.5)
- Addition and subtraction: Estimate sums and differences of whole numbers (Fifth grade - D.10)
- Addition and subtraction: Estimate sums and differences: word problems (Fifth grade - D.11)
- Add and subtract decimals: Estimate sums and differences of decimals (Fifth grade - E.6)
- Multiplication: Multiply numbers ending in zeroes (Fifth grade - F.4)
- Multiplication: Multiply numbers ending in zeroes: word problems (Fifth grade - F.5)
- Multiplication: Estimate products (Fifth grade - F.8)
- Multiplication: Estimate products: word problems (Fifth grade - F.9)
- Multiply decimals: Estimate products of decimals (Fifth grade - G.1)
- Multiply decimals: Multiply a decimal by a power of ten (Fifth grade - G.2)
- Division: Estimate quotients: word problems (Fifth grade - H.6)
- Division: Divide numbers ending in zeroes (Fifth grade - H.8)
- Division: Divide numbers ending in zeroes: word problems (Fifth grade - H.9)
- Division with decimals: Divide by powers of ten (Fifth grade - I.1)

**5.E&C-2 recalling basic multiplication facts, products to 144, and corresponding division facts efficiently****5.E&C-3 adding or subtracting four-digit whole numbers, fractions with like denominators to 12, or decimals involving money**- Addition and subtraction: Add and subtract whole numbers up to billions (Fifth grade - D.1)
- Addition and subtraction: Add and subtract whole numbers: word problems (Fifth grade - D.2)
- Addition and subtraction: Add and subtract money amounts (Fifth grade - D.3)
- Addition and subtraction: Complete addition and subtraction sentences (Fifth grade - D.5)
- Addition and subtraction: Fill in the missing digits (Fifth grade - D.6)
- Add and subtract fractions: Add and subtract fractions with like denominators (Fifth grade - M.1)

**5.E&C-4 multiplying two-digit whole numbers by two-digit numbers or dividing three-digit whole numbers by single-digit numbers**- Multiplication: Multiply by 2-digit numbers: complete the missing steps (Fifth grade - F.10)
- Multiplication: Multiply a 2-digit number by a 2-digit number (Fifth grade - F.11)
- Division: Divide multi-digit numbers by 1-digit numbers (Fifth grade - H.3)
- Division: Divide multi-digit numbers by 1-digit numbers: word problems (Fifth grade - H.4)
- Division: Divide by 1-digit numbers: interpret remainders (Fifth grade - H.5)

**5.F&R-1 extending patterns that use addition, subtraction, multiplication, division or symbols, up to 10 terms, represented by models (function machines), tables, sequences, or in problem situations**- Multiplication: Multiplication patterns over increasing place values (Fifth grade - F.3)
- Division: Division patterns over increasing place values (Fifth grade - H.7)
- Patterns: Patterns involving addition and multiplication (Fifth grade - T.3)
- Patterns: Numeric patterns: word problems (Fifth grade - T.4)

**5.F&R-2 using rules to express the generalization of a pattern using words, lists, or tables****5.F&R-3 identifying or applying addition or subtraction patterns to find missing values in a function****5.F&R-4 using manipulatives, including a calculator, as tools when describing, extending, or representing a number sequence****5.F&R-5 using an open number sentence (addition, subtraction, multiplication, or division) to solve for an unknown represented by a box or circle (e.g., 256 ÷ __ = 8, __ ÷ 8 = 56, 36 ÷ 3 = __)**- Addition and subtraction: Choose numbers with a particular sum or difference (Fifth grade - D.7)
- Multiplication: Choose numbers with a particular product (Fifth grade - F.7)
- Division: Choose numbers with a particular quotient (Fifth grade - H.14)
- Algebra: Evaluate variable expressions (Fifth grade - Q.3)
- Algebra: Solve equations I (Fifth grade - Q.5)
- Algebra: Solve equations II (Fifth grade - Q.6)

**5.G-1 using the attributes and properties of angles and the number, length, and orientation of sides to identify or compare triangles (scalene, isosceles, or equilateral) or quadrilaterals (parallelograms, trapezoids, rhombi)**- Geometry: Types of triangles (Fifth grade - B.2)
- Geometry: Open and closed shapes and qualities of polygons (Fifth grade - B.3)
- Geometry: Regular and irregular polygons (Fifth grade - B.4)
- Geometry: Number of sides in polygons (Fifth grade - B.5)
- Geometry: Which figure is being described? (Fifth grade - B.6)
- Geometry: Types of angles (Fifth grade - B.12)
- Geometry: Find the unknown angle in triangles and quadrilaterals (Fifth grade - B.32)

**5.G-2 using the attributes and properties of solid figures (edges, vertices, number of faces) to model, identify, compare, or describe (cubes, cylinders, cones, spheres, pyramids, or rectangular prisms) (e.g., boxes, buildings, packages)****5.G-3 illustrating or identifying the results of transformation (slides, turns, or flips of polygons) (e.g., pictures of cultural art, fabric designs, architecture, logos)****5.G-4 identifying, creating, or drawing geometric figures that are congruent, similar, or symmetrical****5.G-6 estimating or determining area or perimeter of rectangles using a key, ruler, or given measures****5.G-7 estimating or determining the area and circumference of a circle using a grid or manipulatives****5.G-8 locating points of given coordinates on a grid or identifying coordinates for a given point (e.g., items on a treasure map)****5.G-9 identifying or drawing perpendicular line segments or midpoints****5.S&P-1 designing an investigation and collecting, organizing, or displaying, using appropriate scale, data in real-world problems (e.g., social studies, friends, or school), using bar graphs, tables, charts, diagrams, or line graphs with whole numbers up to 50****5.S&P-2 using information from a variety of displays (tables, bar graphs, line graphs, or Venn diagrams)**- Problem solving: Use Venn diagrams to solve problems (Fifth grade - J.5)
- Data, charts, and graphs: Read a table (Fifth grade - S.1)
- Data, charts, and graphs: Interpret pictographs (Fifth grade - S.6)
- Data, charts, and graphs: Interpret histograms (Fifth grade - S.8)
- Data, charts, and graphs: Frequency charts (Fifth grade - S.12)
- Data, charts, and graphs: Stem-and-leaf plots (Fifth grade - S.13)
- Data, charts, and graphs: Circle graphs (Fifth grade - S.14)

**5.S&P-3 using mode, median, or range with up to 10 pieces of data with a value of 10 or less each****5.S&P-4 predicting or explaining the probability of all possible outcomes in an experiment using ratios or fractions to describe the probability****5.S&P-5 solving or identifying solutions to problems involving money combinations (e.g., how many ways can you make 25 cents using nickels, dimes, or quarters?)**

**5 Understand and be able to select and use a variety of problem-solving strategies**

**5.PS-1 selecting and applying an appropriate strategy (e.g., tables, charts, lists, or graphs; guess and check; extended patterns; make a model) to solve a variety of problems and verify the results**- Problem solving: Multi-step word problems (Fifth grade - J.1)
- Problem solving: Word problems with extra or missing information (Fifth grade - J.2)
- Problem solving: Guess-and-check problems (Fifth grade - J.3)
- Problem solving: Find the order (Fifth grade - J.4)
- Algebra: Graph linear functions (Fifth grade - Q.10)
- Algebra: Evaluate functions (Fifth grade - Q.11)
- Patterns: Geometric growth patterns (Fifth grade - T.1)
- Patterns: Increasing growth patterns (Fifth grade - T.2)
- Time: Schedules and time lines (Fifth grade - X.6)
- Time: Time patterns (Fifth grade - X.7)

**5.PS-3 representing problems using mathematical language including concrete, pictorial, and/or symbolic representation; or organizing and communicating mathematical problem-solving strategies and solutions using mathematical language**